President-elect Donald J. Trump woke up on Tuesday to announce on Twitter that he was canceling a planned meeting with the “failing” New York Times, but would move ahead with meetings to form his government “for the next 8 years.” The news media continues to be his foil of choice._________________Hiromichi

When someone is 'foiled', it means that their plans were stopped (the plans have a negative connotation). For example: "The bank robber's plans were foiled by the police."

I think what they're trying to say is that Trump is choosing to 'foil' the media, as he continues to pick on them. It has a sarcastic connotation to it, though because it's the kind of word you would find in a superhero comic book. It's as if Trump thinks he's very smart in ruining the media's plans, but it doesn't really affect the media at all.

I realize that's a pretty difficult explanation, but I hope it helps! Let me know if I can explain it any further._________________- Roger